Mix the cold and condensed milk in a large bowl until well combined. Add the pudding and stir until mixed well. Chill for 5 minutes so the pudding will thicken. (You can also use a mixer to quickly mix the milk and pudding.)
In a medium bowl, add 2-3 tablespoons of lemon juice. Add the cut bananas and gently stir to coat them with lemon juice. Add more lemon juice if necessary to thoroughly coat the bananas. This will keep them from turning brown. Drain off any excess lemon juice.
Fold the whipped topping into the thickened pudding mixture. Then, in six dessert bowls, layer with pudding, bananas, and a layer of cookies. Repeat until all the pudding mixture is used, ending with a pudding layer. Garnish with extra cookies.
Notes
Make Banana Pudding in One Dish
This dessert can also be layered in a medium-sized bowl or casserole dish. Start by placing 1/3 of the pudding mixture in the bowl and then layer with bananas and cookies. Repeat layers, ending with pudding.
Cookies
There are usually leftover cookies after making this dessert. Making banana pudding in a large dish takes more cookies than in individual bowls.
Substitution
You can substitute whipped cream for whipped topping:
Whip 1 1/2 cups of whipping cream with three tablespoons of sugar to yield the equivalent of 8 ounces of Cool Whip.